The premise of this article is that the study of representation is valuable and important for mathematics and science students. Learning about representation should go beyond learning specific, sanctioned representations emphasized in standard curricula (graphs, tables, etc.) to include principles and design strategies that apply to any scientific representation, including novel variations and even completely new representations. The article explores what it means to understand representation, what we believe students already know about the topic, and what they can profitably learn about it. The discussion includes learning difficulties-goals for instruction that appear challenging for students and may need particular attention.